The range of the gradient of a Lipschitz \(C^1\)-smooth bump in infinite dimensions

DOI10.1007/BF02784514zbMath1010.46016OpenAlexW2089900962MaRDI QIDQ1860708

Martin Fabian, Jonathan M. Borwein, Philip D. Loewen

Publication date: 20 May 2003

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02784514

zbMATH Keywords

bump function

Mathematics Subject Classification ID

Fréchet and Gateaux differentiability in optimization (49J50) Geometry and structure of normed linear spaces (46B20) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (6)

Filling analytic sets by the derivatives of 𝐶¹-smooth bumps ⋮ Smooth approximations without critical points ⋮ A note on the range of the derivatives of analytic approximations of uniformly continuous functions on \(c_0\) ⋮ On the range of the derivative of Gâteaux-smooth functions on separable Banach spaces ⋮ Construction of pathological Gâteaux differentiable functions ⋮ The range of the derivative of a differentiable bump.

Cites Work

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• On smooth, nonlinear surjections of Banach spaces
• A note on norm attaining functionals
• On the size of the sets of gradients of bump functions and starlike bodies on the Hilbert space
• James' theorem fails for starlike bodies
• The failure of Rolle's theorem in infinite-dimensional Banach spaces

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